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Free vibration of the system of two Timoshenko beams coupled by a viscoelastic interlayer

Cabańska-Płaczkiewicz K.

Engineering Transactions

1999

Vol. 47, iss. 1

21-37

In this paper the uniform analytical method [3] has been used for solving a problem of free vibrations of continuous sandwich beam with damping. External layers are modelled as Timoshenko beams, while the internal layer possesses the characteristics of a viscoelastic, one-directional Winkler foundation. The phenomenon of free vibration has been descibed using a homogenous system of coupled partial differential equations. After separation of variables in the system of differential equations, the boundary problem has been solved and four complex sequences have been obtained : the sequences of frequencies, and the sequences of vibration modes. Then, the property of orthogonality of complex free vibration modes has been demonstrated. The free vibration problem has been solved for arbitrarily assumed initial conditions.